Skip to main content
SpringerLink
Log in

Representation Theory for Linear Infinite Dimensional Continuous Time Systems

  • Conference paper
Book cover Mathematical Systems Theory

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 131))

Abstract

Representation theory for finite dimensional systems has been the subject of a great deal of discussion in recent years. In the case of linear systems defined over fields an account of the theory can be found in the books of BROCKETT and KALMAN-FALB-ARBIB and in the case of systems defined over rings in the book of EILENBERG, the papers of ROUCHALEAU-WYMAN-KALMAN, ROUCHALEAU-WYMAN and the thesis of JOHNSTON. For a lucid survey of results on systems defined over commutative rings, see SONTAG.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • AUBIN, J.P, and A . BENSOUSSAN, to appear.

    Google Scholar 

  • BALAKRISHNAN, A.V., Foundations of the State Space Theory of Continuous Systems I, Journal of Computer and System Sciences, 1967.

    Google Scholar 

  • BARAS, J.S., R.W. BROCKETT, and P.A. FUHRMANN, State-Space Models for Infinite-Dimensional Systems, IEEE Transactions on Automatic Control, Vol. AC-19, No. 6, December 1974.

    Google Scholar 

  • BENSOUSSAN, A., M.C. DELFOUR, and S.K. MITTER, Representation and Control of Infinite Dimensional Systems, monograph to appear.

    Google Scholar 

  • BOURBAKI, N., Espaces Vectoriels Topologiques, Chapitre IV, Hermann, Paris, 1964.

    Google Scholar 

  • BROCKETT, R.W., Finite Dimensional Linear Systems, Wiley, New York, 1970.

    MATH  Google Scholar 

  • EILENBERG, S., Automata, Languages, and Machines, Vol. I, Academic Press, 1974.

    MATH  Google Scholar 

  • JOHNSTON, R., Linear Systems Over Various Rings, Ph.D. dissertation, M.I.T., 1973.

    Google Scholar 

  • KALMAN, R.E., P.L. FALB, and M.A. ARBIB, Topics in Mathematical System Theory, McGraw Hill, New York, 1969.

    MATH  Google Scholar 

  • KALMAN, R.E. and M.L.J. HAUTUS, Realization of Continuous-time Linear Dynamical Systems: Rigorous Theory in the Style of Schwartz, in Ordinary Differential Equations, ed. L. Weiss, Academic Press, New York, 1972.

    Google Scholar 

  • KALMAN, R.E. and T. MATSUO, to appear.

    Google Scholar 

  • KAMEN, E.W., On an Algebraic Theory of Systems Defined by Convolution Operators, Math. Systems Theory, Vol. 9, 1975, pp. 57–74.

    Article  MathSciNet  MATH  Google Scholar 

  • ROUCHALEAU, Y. and B.F. WYMAN, Linear dynamical systems over integral domains, J. Comp. Syst. Sci., 9: 129–142, 1975.

    Article  MathSciNet  Google Scholar 

  • ROUCHALEAU, Y., B.F. WYMAN, and R.E. KALMAN, Algebraic structure of linear dynamical systems. III. Realization theory over a commutative ring, Proc. Nat. Acad. Sci. (USA), 69: 3404–3406, 1972.

    Article  MathSciNet  MATH  Google Scholar 

  • SONTAG, E.D., Linear Systems over Commutative Rings: A Survey, to appear in Ricerche di Automatica.

    Google Scholar 

  • TREVES, F., Topological Vector Spaces, Distributions and Kernels, Academic Press, New York, 1967.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Paris IX and Iria-Laboria, Paris, France

    A. Bensoussan

  2. Centre de Recherches Mathematiques, Universitè de Montreal, Montreal, Canada

    M. C. Delfour

  3. Department of Electrical Engineering and Computer Science and Electronic Systems Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts, 02139, USA

    S. K. Mitter

Authors
  1. A. Bensoussan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. C. Delfour
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. K. Mitter
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering, University of Padua, 6/A Via Gradenigo, 35100, Padova, Italy

    Giovanni Marchesini

  2. Department of Electrical Engineering and Computer Science and Electronic Systems Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts, 02139, USA

    Sanjoy Kumar Mitter

Rights and permissions

Reprints and permissions

Copyright information

© 1976 Springer-Verlag Berlin · Heidelberg

About this paper

Cite this paper

Bensoussan, A., Delfour, M.C., Mitter, S.K. (1976). Representation Theory for Linear Infinite Dimensional Continuous Time Systems. In: Marchesini, G., Mitter, S.K. (eds) Mathematical Systems Theory. Lecture Notes in Economics and Mathematical Systems, vol 131. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-48895-5_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-48895-5_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07798-5

  • Online ISBN: 978-3-642-48895-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation